Question

Solve the quadratic equation below using square roots. (x−4)2=25 (1 point) Responses {−1, 9} {−1, 9} {−29−−√, 29−−√} {−29−−√, 29−−√} {−2, 6} {−2, 6} {−3, 7}

Answer 1

To solve the quadratic equation \((x−4)^2=25\) using square roots, follow these steps:

1. Take the square root of both sides:
\[
x - 4 = \pm 5
\]

2. This gives us two cases to solve:

**Case 1:**
\[
x - 4 = 5
\]
\[
x = 5 + 4
\]
\[
x = 9
\]

**Case 2:**
\[
x - 4 = -5
\]
\[
x = -5 + 4
\]
\[
x = -1
\]

3. Therefore, the solutions to the equation are:
\[
x = -1 \quad \text{and} \quad x = 9
\]

The correct response is \(\{-1, 9\}\).